Number-of-particle fluctuations and stability of Bose-Einstein-condensed systems (8 pages)

Vladimir I. Kruglov

David C K Roberts

Андрій Сіжук, Anatoly A. Svidzinsky, Marlan O. Scully

Vyacheslav I. Yukalov

Particle fluctuations in mesoscopic Bose systems of arbitrary spatial dimensionality are considered. Both ideal Bose gases and interacting Bose systems are studied in the regions above the Bose–Einstein condensation temperature T c , as well as below this temperature. The strength of particle fluctuations defines whether the system is stable or not. Stability conditions depend on the spatial dimensionality d and on the confining dimension D of the system. The consideration shows that mesoscopic systems, experiencing Bose–Einstein condensation, are stable when: (i) ideal Bose gas is confined in a rectangular box of spatial dimension d > 2 above T c and in a box of d > 4 below T c ; (ii) ideal Bose gas is confined in a power-law trap of a confining dimension D > 2 above T c and of a confining dimension D > 4 below T c ; (iii) the interacting Bose system is confined in a rectangular box of dimension d > 2 above T c , while below T c , particle interactions stabilize the Bose-condensed system, making it stable for d = 3 ; (iv) nonlocal interactions diminish the condensation temperature, as compared with the fluctuations in a system with contact interactions.

Jesús Manuel Zoido

Vyacheslav I. Yukalov

Fluctuations of the number of particles for the dilute interacting gas with Bose-Einstein condensate are considered. It is shown that in the Bogolubov theory these fluctuations are normal. The fluctuations of condensed as well as noncondensed particles are also normal both in canonical and grand canonical ensembles.